Critical Casimir Interactions and Percolation: the quantitative description of critical fluctuations
arXiv:1604.08842 · doi:10.1103/PhysRevE.98.062138
Abstract
Casimir forces in a critical media are produced by spatial suppression of order parameter fluctuations. In this paper we address the question how fluctuations of a critical media relates the magnitude of critical Casimir interactions. Namely, for the Ising model we express the potential of critical Casimir interactions in terms of Fortuin-Kasteleyn site-bond correlated percolation clusters. These clusters are quantitative representation of fluctuations in the media. New Monte Carlo method for the computation of the Casimir force potential which is based on this relation is proposed. We verify this method by computation of Casimir interactions between two disks for 2D Ising model. The new method is also applied to the investigation of non-additivity of the critical Casimir potential. The non-additive contribution to three-particles interaction is computed as a function of the temperature.
13 pages, 4 figures
References in corpus (13)
- Recent advances in percolation theory and its applications
- The Casimir effect: from quantum to critical fluctuations
- Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
- Monte Carlo simulation results for critical Casimir forces
- Nonadditivity of Critical Casimir Forces
- Thermodynamic Casimir effect for films in the 3D Ising universality class: Symmetry breaking boundary conditions
- Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
- Critical Casimir Forces and Colloidal Phase Transitions in a Near-Critical Solvent : A Simple Model Reveals a Rich Phase Diagram
- Many-body critical Casimir interactions in colloidal suspensions
- Critical Casimir Interactions Between Spherical Particles in the Presence of the Bulk Ordering Fields
- Three-body critical Casimir forces
- Direct simulation of critical Casimir forces
- Casimir interaction of rod-like particles in a two-dimensional critical system